Differential Geometry/notation help

[EV33]

Homework Statement

I have this theorem which I am having trouble understanding due to notation.

Theorem: Define S,S'$\subseteq$ℝ³ to be surfaces. Let f:S→S' be a smooth map. f is a local isometry if for all p in S, and all w₁,w₂ in T_pS,
<w₁,w₂>=<df_p(w₁),df_p(w₂)>.


The thing I don't get, is what does df_p(w₁) mean?
What action is going on between df_p and w₁?


Thank you for your time.

 

[HallsofIvy]

$df_p$ is the derived mapping from the tangent space at p in S to the tangent space at f(p) in S'.